Companion Question on Southwest Airlines

FlyerTalk member milesintexas has a question about bringing a companion on-board a Southwest Airlines flight:

“I know this has probably been asked here before. And I am not trying to cheat the system. But here it goes. I am a companion pass holder. ( My wife designated me her companion). I have also earned a companion pass w/ a 100 credits. (Designated my girlfriend my companion!). If my wife books a ticket, I know I can fly for free. Can my girlfriend fly for free as well?